how to solve a Conditional ODE problem

Grace

2016 5 27

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I am trying to solve a problem involving a neural network type model as shown in the picture.

However g is a conditional function and I am not sure how to incorporate this into an ode solver.

Any help would be appreciated!

my unsuccessful attempt:

clear all
close all
N=50; %number of units (i)
w=zeros(N,N); %synaptic efficiency matrix
a=0.7; %reducing factor alpha
y=[];
t=linspace(0,9,100); %time vector
for i=1:N
K=randi([0 N-1],1,1); %selects K (j) out of N-1 units acting on unit i
w(i,:)=[zeros(1,N-K),ones(1,K)]*-1; %sets corresponding i,j of connection matrix to -1 indicating connection, otherwise set to 0 (no connection)
w(i,:)=w(:,1)(randperm(N)); %randomly orders connections
end
for i=1:N
for j=1:N
if w(i,j)==-1;
w(j,i)=0;
end  %if already a connection between j action on i cannot be connect for i acting on j
end
end
R = normrnd(0,.001,1,N); %mean of 0 std .001
tau=-(K-1.5)*[R]; %generation of threshold vector
tau=tau' %convert to column vector
d=randi([0 N-1],1,1) ; 
for k=1:d
w(:,k)=w(:,k)*a;
end %synapse connection defficiency in first random d columns
g=zeros(1,N)
function dy = ODE(t,y)
for i=1:N
sum=0;
for j=1:N
if y(j)<0
g(j)=0
else
g(j)=1
sum=sum+(w(i,j)*g(j)
end
dy(i) = -y(i)+sum-tau(i);
end
endfunction
[t,y]=ode45(dy,t,1);